A country has been experiencing a mean of 34.6 motor vehicle deaths each year. U
ID: 3129936 • Letter: A
Question
A country has been experiencing a mean of 34.6 motor vehicle deaths each year. Use the Poisson Distribution to answer the following
a. Mean number of deaths per day___________________ round to three decimal places as needed.
b. The probability of more than two motor vehicole deaths on a given day is___________________round to six decimal places as needed.
c. Let the probability of 0.05 or less denote an unusual event choose the correct answer below
A Yes it is unusual, the probability of there being more than two motor vehicle deaths on the same day is less than 1.
B Yes it is unusual. The probability of there being more than two motor vehicle deaths on the same day is very small
C, No it is not unusual. The probability of there being more than two motor vehicle deaths on the same day is greater than 0
D No it is not unusual. The probability of there being more than two motor vehicle deaths on the same day is very small.
Explanation / Answer
a)
There are 34.6 deaths a year (365 days), so there are 34.6/365 = 0.094794521 deaths a day.
ANSWEr: 0.095 [ANSWER]
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b)
Note that P(more than x) = 1 - P(at most x).
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 0.094794521
x = our critical value of successes = 2
Then the cumulative probability of P(at most x) from a table/technology is
P(at most 2 ) = 0.99986775
Thus, the probability of at least 3 successes is
P(more than 2 ) = 0.00013225 [ANSWER]
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c)
OPTION B: B Yes it is unusual. The probability of there being more than two motor vehicle deaths on the same day is very small. [ANSWER]
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